Ayura is offered mortgage rates of 4.13% on a 15-year and 4.70% on a 30-year. She...

Ayura is offered mortgage rates of 4.13% on a 15-year and 4.70% on a 30-year. She is able to make either payment and is buying a house with an initial loan balance of $245,000. Her lender is offering 1.5 discount points and she will pay $8,700 is third party expenses. If she is able to earn 10.9% investing in the S&P 500.

Then a. What is her monthly payment for each loan?

b. What is the lender's yield on each loan?

c. What is the effective borrowing cost of each loan?

d. Based on present value computations which loan is a better option for her?

Expert Solution


a.	MONTHLY PAYMENT IN EACH LOAN

	4.13% 15 year Loan
	Loan amount	$245,000
	Discount point payment	$3,675	(0.015*245000)
	Third Party expense	$8,700
	Monthly interest	(4.13/12)%
	Number of months of payment	180	(15*12)
	Monthly Payment	$1,828.24	(Using PMT Function with Rate=(4.13/12)%,Nper=180,PV=-245000)

	4.7% 30 year Loan
	Loan amount	$245,000
	Discount point payment	$3,675	(0.015*245000)
	Third Party expense	$8,700
	Monthly interest	(4.7/12)%
	Number of months of payment	360	(30*12)
	Monthly Payment	$1,270.66	(Using PMT Function with Rate=(4.7/12)%,Nper=360,PV=-245000)

b.	Lender's Yield
	4.13% 15 year loan
	Net Initialcash Flow	($241,325)	(245000-3675)
	Cash inflow per month	$1,828.24
	Number of months	180
	Lender's Monthly Yield	0.363%	(Using RATE function of excel with Nper=180,Pmt=1828.24,PV=-241325)
	Lender's Annual Yield	4.35%	(0.363*12)

	4.7% 30 year Loan
	Net Initialcash Flow	($241,325)	(245000-3675)
	Cash inflow per month	$1,270.66
	Number of months	360
	Lender's Monthly Yield	0.403%	(Using RATE function of excel with Nper=360,Pmt=1270.66,PV=-241325)
	Lender's Annual Yield	4.83%	(0.403*12)

c	Effective borrowing Cost
	4.13% 15 year loan
	Net Initialcash Flow to borrower	$232,625	(245000-3675-8700)
	Cash out flow per month	($1,828.24)
	Number of months	180
	Effective borrowing Cost	0.409%	(Using RATE function of excel with Nper=180,Pmt=1828.24,PV=-241325)
	AnnualBorrowing Cost	4.91%	(0.409*12)

	4.7% 30 year Loan
	Net Initial cash Flow to borrower	$232,625	(245000-3675)
	Cash outflow per month	($1,270.66)
	Number of months	360
	Effective Borrowing Cost	0.429%	(Using RATE function of excel with Nper=360,Pmt=1270.66,PV=-232625)
	Annualborrowing cost	5.15%	(0.429*12)

d	Present Value calculation:
	4.13% 15 year Loan
	Monthly payment	$1,828.24
	Number of months	180
	Discount Rate per month	(10.9/12)%
	Present Value of Loan Repayments	$161,744.57	(Using PV function of excel with Rate=(10.9/12)%, Nper=180, Pmt=-1828.24)

	4.7% 30 year Loan
	Monthly payment	$1,270.66
	Number of months	360
	Discount Rate per month	(10.9/12)%
	Present Value of Loan Repayments	$134,493.42	(Using PV function of excel with Rate=(10.9/12)%, Nper=360, Pmt=-1270.66)

	4.7% 30 year Loan is cheaper option

jeff jeffy answered 2 years ago

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